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International Journal of Control
74 (11), pp. 1131-1139 (July 20, 2001)

Abstract

This paper examines the fundamental limitations imposed by unstable (Right Half Plane; RHP) zeros and poles in multivariable feedback systems. We generalize previously known controller-independent lower bounds on the H-infinity-norm of closed-loop transfer functions WXV , || WXV (s)||_infinity, where X is input or output sensitivity or complementary sensitivity, to include multivariable unstable and non-minimum phase weights W and V . The bounds are tight for cases with only one RHP-zero or pole. For plants with RHP-zeros we obtain bounds on the output performance for reference tracking and disturbance rejection. For plants with RHP-poles we obtain new bounds on the input performance. This quantifies the minimum input usage needed to stabilize an unstable plant in the presence of disturbances or noise. For a one degree-of-freedom controller the combined effect of RHP-zeros and poles further deteriorate the output performance, whereas there is no such additional penalty with a two degrees-of-freedom controller where also the disturbance and/or reference signal is used by the controller.